what about this one matheagle? i thanked you for your other ones
Machines I and II respectively produce 70% and 30% of a factory’s output. Machine I produces 2% defectives and machine II produces 3% defectives. If an item is not defective, what is the chance it was produced by machine I?
Which event would be A and which one B?
I will let A stand for machine one and B for machine 2.
You have and as the partition.
Next you have and where D stands for defective.
So the probability of defective is
Hence the probability of a NONdefective is .977.
Let N stand for nondefective. The question here is .
We have and from
we can obtain since from above.
I get .702149437 for the final answer, which seems reasonable since P(A)=.7 isn't far away.